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A036136 a(n) = 3^n mod 89.

%I A036136 #18 Sep 08 2022 08:44:52
%S A036136 1,3,9,27,81,65,17,51,64,14,42,37,22,66,20,60,2,6,18,54,73,41,34,13,
%T A036136 39,28,84,74,44,43,40,31,4,12,36,19,57,82,68,26,78,56,79,59,88,86,80,
%U A036136 62,8,24,72,38,25,75,47,52,67,23
%N A036136 a(n) = 3^n mod 89.
%D A036136 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036136 G. C. Greubel, <a href="/A036136/b036136.txt">Table of n, a(n) for n = 0..10000</a>
%H A036136 <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
%F A036136 From _G. C. Greubel_, Oct 17 2018: (Start)
%F A036136 a(n) = a(n-1) - a(n-44) + a(n-45).
%F A036136 a(n+88) = a(n). (End)
%p A036136 [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036136 PowerMod[3, Range[0, 100], 89] (* _G. C. Greubel_, Oct 17 2018 *)
%o A036136 (PARI) a(n)=lift(Mod(3,89)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036136 (Magma) [Modexp(3, n, 89): n in [0..100]]; // _G. C. Greubel_, Oct 17 2018
%o A036136 (Python) for n in range(0, 100): print(int(pow(3, n, 89)), end=' ') # _Stefano Spezia_, Oct 17 2018
%o A036136 (GAP) List([0..60],n->PowerMod(3,n,89)); # _Muniru A Asiru_, Oct 17 2018
%Y A036136 Cf. A000244 (3^n).
%K A036136 nonn,easy
%O A036136 0,2
%A A036136 _N. J. A. Sloane_